A structure-preserving split finite element discretization of the split wave equations

We introduce a new finite element (FE) discretization framework applicable for covariant split equations. The introduction of additional differential forms (DF) that form pairs with the original ones permits the splitting of the equations into topological momentum and continuity equations and metric-dependent closure equations that apply the Hodge-star operator. Our discretization framework conserves this geometrical structure and provides for all DFs proper FE spaces such that the differential operators hold in strong form. We introduce lowest possible order discretizations of the split 1D wave equations, in which the discrete momentum and continuity equations follow by trivial projections onto piecewise constant FE spaces, omitting partial integrations. Approximating the Hodge-star by nontrivial Galerkin projections (GP), the two discrete metric equations follow by projections onto either the piecewise constant (GP0) or piecewise linear (GP1) space. Our framework gives us three schemes with significantly different behavior. The split scheme using twice GP1 is unstable and shares the dispersion relation with the P1-P1 FE scheme that approximates both variables by piecewise linear spaces (P1). The split schemes that apply a mixture of GP1 and GP0 share the dispersion relation with the stable P1-P0 FE scheme that applies piecewise linear and piecewise constant (P0) spaces. However, the split schemes exhibit second order convergence for both quantities of interest. For the split scheme applying twice GP0, we are not aware of a corresponding standard formulation to compare with. Though it does not provide a satisfactory approximation of the dispersion relation as short waves are propagated much too fast, the discovery of the new scheme illustrates the potential of our discretization framework as a toolbox to study and find FE schemes by new combinations of FE spaces

E-cadherin and APC compete for the interaction with beta-catenin and the cytoskeleton

beta-Catenin is involved in the formation of adherens junctions of mammalian epithelia. It interacts with the cell adhesion molecule E-cadherin and also with the tumor suppressor gene product APC, and the Drosophila homologue of beta-catenin, armadillo, mediates morphogenetic signals. We demonstrate here that E-cadherin and APC directly compete for binding to the internal, armadillo-like repeats of beta-catenin; the NH2-terminal domain of beta-catenin mediates the interaction of the alternative E-cadherin and APC complexes to the cytoskeleton by binding to alpha-catenin. Plakoglobin (gamma-catenin), which is structurally related to beta-catenin, mediates identical interactions. We thus show that the APC tumor suppressor gene product forms strikingly similar associations as found in cell junctions and suggest that beta-catenin and plakoglobin are central regulators of cell adhesion, cytoskeletal interaction, and tumor suppression

A structure-preserving approximation of the discrete split rotating shallow water equations

We introduce an efficient split finite element (FE) discretization of a y-independent (slice) model of the rotating shallow water equations. The study of this slice model provides insight towards developing schemes for the full 2D case. Using the split Hamiltonian FE framework [1,2], we result in structure-preserving discretizations that are split into topological prognostic and metric-dependent closure equations. This splitting also accounts for the schemes' properties: the Poisson bracket is responsible for conserving energy (Hamiltonian) as well as mass, potential vorticity and enstrophy (Casimirs), independently from the realizations of the metric closure equations. The latter, in turn, determine accuracy, stability, convergence and discrete dispersion properties. We exploit this splitting to introduce structure-preserving approximations of the mass matrices in the metric equations avoiding to solve linear systems. We obtain a fully structure-preserving scheme with increased efficiency by a factor of two

Wave conditions in the Baltic Proper and in the Gulf of Finland during windstorm Gudrun

International audienceWave conditions in the northern Baltic Proper during windstorm Erwin/Gudrun (January 2005) are analysed based on in situ measurements in three locations and output of operational wave models from the German Weather Forecast Service, the Danish Meteorological Institute and the Finnish Institute of Marine Research. The measured significant wave height reached 7.2 m in the northern Baltic Proper and 4.5 m in the Gulf of Finland. The roughest wave conditions, estimated from the comparison of the forecast and measured data, occurred remote from the sensors, off the coasts of Saaremaa and Latvia where the significant wave height was about 9.5 m. Peak periods exceeded 12 s in a large part of the northern Baltic Proper and in the central part of the Gulf of Finland

Microstructure and wear behaviour of high alloyed hot-work tool steels 1.2343 and 1.2367 under thermo-mechanical loading

Tools and their maintenance costs in hot forging processes account for a considerable proportion of the total components' costs. Forging tools undergo extreme heating and subsequent cooling during the forging process and between the forging cycles, respectively. This cyclic heating and cooling of the tool surfaces leads to local changes in the tool microstructure which result in hardening or softening of the material in different regions of the tool and consequently influence the tool strength. Temperature in the tool areas experiencing high thermo-mechanical loadings can exceed the austenitic temperature. Hence, a strong cooling, for example by spraying or lubrication, can lead to formation of a martensitic layer in the boundary zone of the tool. Due to its higher hardness, martensitic layer has greater resistance to wear as compared to the basic or tempered materials. In the scope of this paper, the austenitisation behaviours of two high alloyed hot-work tool steels, 1.2343 and 1.2367, have been characterized by means of dilatometer tests to obtain time-temperature-austenitisation (TTA) diagrams for specimen under thermo-mechanical loads. Moreover, continuous-cooling-transformation (CCT) diagrams were recorded. Metallographic investigations were carried out to gather a detailed understanding of the microstructure behaviour and its resulting hardness. With the results of this works, it is aimed to gather a detailed and accurate insight into the arising hardening and softening effects. This would eventually lead to an optimisation of the numerical modelling for tool wear prediction

Inclusive Quasi-Elastic Charged-Current Neutrino-Nucleus Reactions

The Quasi-Elastic (QE) contribution of the nuclear inclusive electron scattering model developed in Nucl. Phys. A627 (1997) 543 is extended to the study of electroweak Charged Current (CC) induced nuclear reactions, at intermediate energies of interest for future neutrino oscillation experiments. The model accounts for, among other nuclear effects, long range nuclear (RPA) correlations, Final State Interaction (FSI) and Coulomb corrections. Predictions for the inclusive muon capture in $^{12}$C and the reaction $^{12}$C $(\nu_\mu,\mu^-)X$ near threshold are also given. RPA correlations are shown to play a crucial role and their inclusion leads to one of the best existing simultaneous description of both processes, with accuracies of the order of 10-15% per cent for the muon capture rate and even better for the LSND measurement.Comment: 31 pages and 14 figures, accepted for publication as a regular article in Physical Review

E-cadherin and APC compete for the interaction with beta-catenin and the cytoskeleton.

beta-Catenin is involved in the formation of adherens junctions of mammalian epithelia. It interacts with the cell adhesion molecule E-cadherin and also with the tumor suppressor gene product APC, and the Drosophila homologue of beta-catenin, armadillo, mediates morphogenetic signals. We demonstrate here that E-cadherin and APC directly compete for binding to the internal, armadillo-like repeats of beta-catenin; the NH2-terminal domain of beta-catenin mediates the interaction of the alternative E-cadherin and APC complexes to the cytoskeleton by binding to alpha-catenin. Plakoglobin (gamma-catenin), which is structurally related to beta-catenin, mediates identical interactions. We thus show that the APC tumor suppressor gene product forms strikingly similar associations as found in cell junctions and suggest that beta-catenin and plakoglobin are central regulators of cell adhesion, cytoskeletal interaction, and tumor suppression

Semileptonic B Decays and Determination of |Vub|

Semileptonic decays of the B mesons provide an excellent probe for the weak and strong interactions of the bottom quark. The large data samples collected at the B Factories have pushed the experimental studies of the semileptonic B decays to a new height and stimulated significant theoretical developments. I review recent progresses in this fast-evolving field, with an emphasis on the determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element |Vub|.Comment: 16 pages, 4 figures, accepted by Mod. Phys. Lett.